Review of Model Order Reduction Methods and Their Applications in Aeroelasticity Loads Analysis for Design Optimization of Complex Airframes

Abstract

Identification of an aircraft critical loads envelope requires a lengthy and rigorous analysis procedure that includes simulating the aircraft in thousands of load cases identified in certification requirements. Imposing a global finite-element model (GFEM) in this process is computationally very expensive, so reduced order models (ROMs) of airframes are commonly used, particularly in iterative static and dynamic aeroelasticity analyses. ROMs must be simple enough to be analyzed thousands of times during a iterative aeroelastic simulation but accurate enough to have dynamic characteristics closely matching those of the GFEM within a frequency range of interest. This paper reviews various techniques of model order reduction (MOR) available in the literature including stiffness extraction by unitary loadings, which is commonly used in the aerospace industry, and linear algebraic matrix-based reduction methodologies. This article presents a case study where the discussed MOR methodologies are used in normal-mode analysis, static, and dynamic aeroelasticity loads analyses of a Bombardier aircraft platform to demonstrate the efficiency of each ROM reviewed. Results obtained show that a ROM generated using component mode synthesis (CMS) has superior dynamic characteristics compared to all other reduction methods reviewed. Compared to the GFEM, it is found that errors in RMS values of loads recovered using the fixed and free interface CMS ROM subject to tuned discrete gust are 1.17% and 1.14%, respectively. Similarly, errors found in the RMS values of the magnitude of loads recovered due to von Karman power spectral density gust are 0.56% and 0.75% for the fixed and free interface CMS ROM, respectively.